My dictionary lists 髭 as moustache / beard, but from the example sentences in WWWJDIC, it seems like 髭 is more often used to mean "beard" than "moustache" ?
So for example, in this sentence: 彼はもっと大人に見えるようにひげをはやした。, is it clear to the listener that the speaker wanted to say "He grew a beard to look more mature", and not "He grew mustache to look more mature"? Or is it ambiguous and it could mean either one?
Your example says he grew facial hair. If it's a Japanese person, I would even dare say that it unambiguously refers to a beard, since I haven't seen many moustaches recently in Japan (beside mines), while I keep seeing guys struggling to get a beard :)
The unambiguous words you can use are:
In a Japanese context, that distinction does not matter so much, and it can be either. Since you are asking whether that Japanese word is ambiguous, I think that you are biased to English mind. It is not that the word 髭 is ambiguous; it is that a single concept in English does not match a single concept in Japanese. This is similar to fingers vs. thumbs. English makes that distinction, but Japanese does not. So there is no one-to-one correspondence. You cannot say that the Japanese word 指 is ambiguous. It is simply that the two languages segment the world into concepts in a different way.
But if you were to say which one is more typically called 髭, then I would say it is moustache. If you want to specifically refer to beard, you can say 顎髭 'chin-moustache/beard'.
I'm a Japanese native speaker. It's my impression that in the aforementioned sentence 'hige' is very ambiguous, floating somewhere between beard and mustache. To be honest I don't give much thought to the difference in reading/hearing such a sentence.
I don't fully agree with the idea that 'hige' is more likely to indicate mustache, although Sawa's explanation on the difference of range each language can cover truly tally with my idea. In fact, aside from 'ago-hige', which as shown in the comment denotes beard, we also have 'kuchi-hige', which means mustache.
So let me put it this way: in saying 'hige', we tend to think that it's just some amount of hair covering the part around our mouth, thick or sparse. In order to indicate the particular part, you need 'kuchi-' or 'ago-' right before 'hige'.
I think it's hard to tell since they're both read as ひげ.
But comparing to Chinese,
須(simplified) 鬚(traditional) (both read as xū) is used for beard.
髭(zī) is used for moustache.
If you look in the Japanese dictionary, ひげ has two kanji - 鬚 and 髭
The former corresponds to the Chinese word for beard, and the latter for moustache.
